U.S. patent application number 15/579753 was filed with the patent office on 2018-06-28 for automated mobile geotechnical mapping.
The applicant listed for this patent is Queen's University at Kingston. Invention is credited to Marc Gallant, Joshua Marshall.
Application Number | 20180180415 15/579753 |
Document ID | / |
Family ID | 57502861 |
Filed Date | 2018-06-28 |
United States Patent
Application |
20180180415 |
Kind Code |
A1 |
Gallant; Marc ; et
al. |
June 28, 2018 |
Automated Mobile Geotechnical Mapping
Abstract
Provided are apparatus and methods for generating a
representation of a physical environment, comprising: a mobile
sensor platform (MSP) including sensors that output sensor signals
relating to parameters such as range, gravity, direction of the
Earth's magnetic field, and angular velocity. The MSP is adapted to
be moved through the environment. The sensor signals are processed
and observations of axes in the environment are generated for a
sequence of time steps, the orientation of the MSP is estimated for
each of the time steps, observed axes are identified at each
orientation, and similar axes are associated. The orientations, the
axes in the environment, and the directions of gravity and the
Earth's magnetic field are linked such that each observation is
predicted based on the estimates of the orientations. An estimate
of the orientations is optimized and an output of the
representation of the physical environment is generated based on
the optimized orientation estimates. The output may be an axis map,
a visual representation, and/or a data set. In one embodiment the
output device may produce an output comprising a stereonet.
Inventors: |
Gallant; Marc; (Kingston,
CA) ; Marshall; Joshua; (Kingston, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Queen's University at Kingston |
Kingston |
|
CA |
|
|
Family ID: |
57502861 |
Appl. No.: |
15/579753 |
Filed: |
June 10, 2016 |
PCT Filed: |
June 10, 2016 |
PCT NO: |
PCT/CA2016/050664 |
371 Date: |
December 5, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62174372 |
Jun 11, 2015 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01B 11/24 20130101;
G01V 7/00 20130101; G01C 15/00 20130101; G01C 21/20 20130101; G01C
17/16 20130101; G01V 3/40 20130101; G01V 7/06 20130101; G01C 21/165
20130101; G01S 17/89 20130101 |
International
Class: |
G01C 15/00 20060101
G01C015/00; G01V 3/40 20060101 G01V003/40; G01V 7/06 20060101
G01V007/06 |
Claims
1. Apparatus for generating a representation of a physical
environment, comprising: a mobile sensor platform (MSP) including
sensors that output sensor signals, wherein the sensors sense
and/or measure range, gravity, direction of the Earth's magnetic
field, and angular velocity, and the MSP is adapted to be moved
through the environment; a processor that: (i) receives the sensor
signals and generates observations of axes in the environment for a
sequence of time steps; (ii) estimates orientation of the MSP for
each time of the sequence of time steps, identifies observed axes
at each orientation, and associates similar axes; and (iii) links
the orientations, the axes in the environment, and the directions
of gravity and the Earth's magnetic field, such that each
observation is predicted based on the estimates of the
orientations, and optimizes an estimate of the orientations; and an
output device that outputs the representation of the physical
environment based on the optimized orientation estimates.
2. The apparatus of claim 1, wherein the processor builds a graph
that links the orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field.
3. The apparatus of claim 1, wherein the processor optimizes an
estimate of the orientations by minimizing errors between the
predictions and the observations.
4. The apparatus of claim 1, wherein the output device produces an
output including one or more of an axis map, a visual
representation, and a data set.
5. The apparatus of claim 1, wherein the output device produces an
output comprising a stereonet.
6. The apparatus of claim 5, wherein the output device produces the
stereonet by transforming the observed axes to a global coordinate
frame using the optimized orientation estimates.
7. The apparatus of claim 1, wherein the MSP is adapted to he moved
through the environment so that axes to be mapped are captured by a
field of view of the range sensor.
8. The apparatus of claim 1, wherein the MSP is a handheld device,
a robot, an unmanned aerial vehicle, or a non-robotic vehicle.
9. The apparatus of claim 1, wherein the sensors comprise a range
sensor, a three-axis accelerometer, a three-axis gyroscope, and a
three-axis magnetometer,
10. The apparatus of claim 1, wherein the range sensor comprises a
scanning laser rangefinder, LiDAR, time of flight (ToF) camera,
stereo camera system, or other range sensing device.
11. The apparatus of claim 1, wherein the physical environment
comprises a rock face.
12. Programmed media for use with a computer, the programmed media
comprising a computer program stored on non-transitory storage
media compatible with the computer, the computer program containing
instructions to direct the computer to perform one or more of:
receive at least one sensor signal from at least one sensor
associated with a MSP; process the one or more sensor signals and
generate observations of axes in an environment for a sequence of
time steps; estimate orientation of the MSP for each time of the
sequence of time steps, identify observed axes at each orientation,
and associate similar axes; link the orientations, the axes in the
environment, and the directions of gravity and the Earth's magnetic
field, such that each observation is predicted based on the
estimates of the orientations, and optimize an estimate of the
orientations; and output a representation of the optimized
orientation estimates.
13. The programmed media of claim 12, wherein the programmed media
directs the computer to receive sensor signals from sensors
comprising a range sensor, a three-axis accelerometer, a three-axis
gyroscope, and a three-axis magnetometer of the MSP.
14. The programmed media of claim 12, wherein the output comprises
an axis map.
15. Programmed media for use with a computer, the programmed media
comprising a computer program stored on non-transitory storage
media compatible with the computer, the computer program containing
instructions to direct the computer to perform one or more of:
receive data corresponding to observations of axes in an
environment for a sequence of time steps and estimates of
orientation of a MSP for each time of the sequence of time steps;
identify observed axes at each orientation, and associate similar
axes; link the orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field, such that
each observation is predicted based on the estimates of the
orientations, and optimize an estimate of the orientations; and
output a representation of the optimized orientation estimates.
16. The programmed media of claim 15, wherein the output comprises
an axis map.
17. A method for generating an axis map of a physical environment,
comprising; using a mobile sensor platform (MSP) including sensors
that output sensor signals, wherein the sensors sense and/or
measure range, gravity, direction of the Earth's magnetic field,
and angular velocity, and the MSP is adapted to be moved through
the environment; using a processor to: (i) receive the sensor
signals and generate observations of axes in the environment for a
sequence of time steps; (ii) estimate orientation of the MSP for
each time of the sequence of time steps, identify observed axes at
each orientation, and associate similar axes; and (iii) link the
orientations, the axes in the environment, and the directions of
gravity and the Earth's magnetic field, such that each observation
is predicted based on the estimates of the orientations, and
optimize an estimate of the orientations; and output a
representation of the optimized orientation estimates.
18. The method of claim 17, wherein the processor builds a graph
that links the orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field.
19. The method of claim 17, wherein the processor optimizes an
estimate of the orientations by minimizing errors between the
predictions and the observations.
20. The method of claim 17, comprising producing an output
including one or more of an axis map, a visual representation, and
a data set.
21. The method of claim 17, comprising producing a stereonet.
22. The method of claim 21, comprising producing the stereonet by
transforming the observed axes to a global coordinate frame using
the optimized orientation estimates.
23. The method of claim 17, comprising moving the MSP through the
environment so that axes to be mapped are captured by a field of
view of the range sensor.
24. The method of claim 17, wherein the MSP is a handheld device, a
robot, an unmanned aerial vehicle, or a non-robotic vehicle.
25. The method of claim 17, wherein the sensors comprise a range
sensor, a three-axis accelerometer, a three-axis gyroscope, and a
three-axis magnetometer,
26. The method of claim 17, wherein the range sensor comprises a
scanning laser rangefinder, LiDAR, time of flight (ToF) camera,
stereo camera system, or other range sensing device.
27. The method of claim 17, wherein the physical environment
comprises a rock face.
Description
FIELD
[0001] This invention relates generally to the measurement of the
orientations of planes in a physical environment. More
specifically, this invention relates to apparatus and methods for
remote, mobile, automated measurement of the orientations of planes
in a physical environment. The invention is particularly suitable
for use in mining, civil, and geological applications.
BACKGROUND
[0002] A safe, efficient, and accurate method to measure the
properties of rock masses is critical in many engineering and
geological applications. Such applications include ensuring a
stable foundation for civil and geotechnical engineering projects
(e.g., constructing highways, buildings, and bridges), building
safe and efficient mines (e.g., tunnel excavation, rock wall
maintenance), and geological surveys (e.g., mapping to better
understand the properties and evolution of geological features).
Rock masses have highly anisotropic properties due to the existence
of planes of weakness (i.e., discontinuities) caused by tectonic
activity, heating and cooling events, or sudden changes in stress.
These properties are important because they largely determine the
mechanical behaviour, such as stress and displacement, of the rock
mass. For example, there may be a reduction of shear strength along
a discontinuity, and the tensile strength across a discontinuity is
nearly zero. Also, the distribution of discontinuities heavily
affects permeability, influencing how fluids flow through a rock
mass.
[0003] Discontinuities are often visible in rock faces as planar
surfaces, whose orientations may be parameterized using axes. The
same discontinuity may appear as a set of axes (i.e., a joint set)
that have similar orientations. In general, a limited number of
joint sets are visible in a rock face, each statistically
distributed in orientation and spacing. A joint set has a number of
measurable properties from which engineering or geological
information can be inferred. These include its orientation, spacing
(i.e., perpendicular distance between planes in the same joint
set), roughness, and persistence (i.e., the extent of a joint set
in a rock mass of a pre-defined volume). Of particular importance
in characterizing a rock mass, and perhaps the most commonly
measured characteristic, is the orientation of its joint sets, as
this indicates the most likely planes of failure. A commonly used
geological parameterization of a discontinuity plane is its strike
and dip. These two quantities are the azimuth angle of the strike
line of the plane (strike), and the angle relative to the plane
whose normal is the gravity vector (dip) (see FIG. 1). Although an
experienced field geologist or geotechnical engineer can sometimes
qualitatively assess the probable mechanical behaviour of a rock
mass by studying a rock face, quantitative assessment is necessary
for engineering projects or safety considerations.
[0004] Measuring the orientations of joint sets can generally be a
complex, time-consuming, laborious, and often dangerous endeavour.
The most widely used method to measure the strikes and dips of
discontinuity planes in a rock face is by manually measuring
individual planes with a compass (to measure strike) and an
inclinometer (to measure dip). Attempts to automate the process
involve scanning a rock face with a stationary 3D light detection
and ranging (LiDAR) device and processing the resulting point cloud
to estimate the strikes and dips of the discontinuity planes.
However, this method has not yet been widely adopted, possibly due
to drawbacks such as complexity, time requirements, and high
cost.
SUMMARY
[0005] According to one aspect of the invention there is provided
an apparatus for generating a representation of a physical
environment, comprising: a mobile sensor platform (MSP) including
sensors that output sensor signals, wherein the sensors sense
and/or measure range, gravity, direction of the Earth's magnetic
field, and angular velocity, and the MSP is adapted to be moved
through the environment; a processor that: (i) receives the sensor
signals and generates observations of axes in the environment for a
sequence of time steps; (ii) estimates orientation of the MSP for
each time of the sequence of time steps, identifies observed axes
at each orientation, and associates similar axes; and (iii) links
the orientations, the axes in the environment, and the directions
of gravity and the Earth's magnetic field, such that each
observation is predicted based on the estimates of the
orientations, and optimizes an estimate of the orientations; and an
output device that outputs the representation of the physical
environment based on the optimized orientation estimates.
[0006] The apparatus may include an output device that produces an
output including one or more of an axis map, a visual
representation, and a data set. In one embodiment the output device
may produce an output comprising a stereonet.
[0007] The MSP may comprise a handheld device, a robotic vehicle,
an unmanned aerial vehicle, or a non-robotic vehicle. The sensors
may comprise a range sensor i.e., a device that can measure range
in three dimensions, such as a flash LiDAR, a scanner, or a camera;
which may also be referred to as a 3D distance sensor), a
three-axis accelerometer, a three-axis gyroscope, and a three-axis
magnetometer.
[0008] The physical environment may comprise a rock face or a
man-made structure.
[0009] According to another aspect there is provided programmed
media for use with a computer, the programmed media comprising a
computer program stored on non-transitory storage media compatible
with the computer, the computer program containing instructions to
direct the computer to perform one or more of: receive at least one
sensor signal from at least one sensor associated with a MSP;
process the one or more sensor signals and generate observations of
axes in an environment for a sequence of time steps; estimate
orientation of the MSP for each time of the sequence of time steps,
identify observed axes at each orientation, and associate similar
axes; link the orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field, such that
each observation is predicted based on the estimates of the
orientations, and optimize an estimate of the orientations; and
output a representation of the optimized orientation estimates. In
one embodiment the output comprises an axis map.
[0010] Another aspect relates to programmed media for use with a
computer, the programmed media comprising a computer program stored
on non-transitory storage media compatible with the computer, the
computer program containing instructions to direct the computer to
perform one or more of: receive data corresponding to observations
of axes in an environment for a sequence of time steps and
estimates of orientation of a MSP for each time of the sequence of
time steps; identify observed axes at each orientation, and
associate similar axes; link the orientations, the axes in the
environment, and the directions of gravity and the Earth's magnetic
field, such that each observation is predicted based on the
estimates of the orientations, and optimize an estimate of the
orientations; and output a representation of the optimized
orientation estimates. In one embodiment the output comprises an
axis map.
[0011] Another aspect relates to a method for generating an axis
map of a physical environment, comprising; using a mobile sensor
platform (MSP) including sensors that output sensor signals,
wherein the sensors sense and/or measure range, gravity, direction
of the Earth's magnetic field, and angular velocity, and the MSP is
adapted to be moved through the environment; using a processor to:
(i) receive the sensor signals and generate observations of axes in
the environment for a sequence of time steps; (ii) estimate
orientation of the MSP for each time of the sequence of time steps,
identify observed axes at each orientation, and associate similar
axes; and (iii) link the orientations, the axes in the environment,
and the directions of gravity and the Earth's magnetic field, such
that each observation is predicted based on the estimates of the
orientations, and optimize an estimate of the orientations; and
output a representation of the optimized orientation estimates.
[0012] In one embodiment the method comprises producing an output
including one or more of an axis map, a visual representation, and
a data set. In one embodiment the method comprises producing a
stereonet.
[0013] In one embodiment the method comprises moving the MSP
through the environment so that axes to be mapped are captured by a
field of view of the range sensor, wherein the physical environment
comprises a rock face.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] For a greater understanding of the invention, and to show
more clearly how it may be carried into effect, embodiments will be
described, by way of example, with reference to the accompanying
drawings, wherein:
[0015] FIG. 1 is an illustration showing the strike and dip angles
of a plane in a rock mass, wherein the strike is the azimuth
(compass) angle measured from the strike line (shown as a dashed
line) of the plane, and the dip is the angle relative to the
horizontal;
[0016] FIG. 2A is a diagram showing two types of stereonets: a
polar projection (left), and an equal area (Wulff) projection
(right), wherein a plane with orientation 030/40 is plotted as a
square and a dashed line on the polar and equal area projections,
respectively, and a plane with orientation 160/60 is plotted as a
triangle and a dash-dotted line, according to an example;
[0017] FIG. 2B is a diagram showing three different joint sets
plotted on a polar stereonet prior to clustering (left) after
clustering (right), wherein outliers that were removed prior to
clustering are represented by stars; according to an example;
[0018] FIG. 3 is a 2D illustration showing a difference between
conventional landmark-based state estimation (top) and axis mapping
(bottom), according to one embodiment;
[0019] FIG. 4 is an illustration of a rotation vector .theta.,
according to an embodiment;
[0020] FIG. 5A is a diagram showing global parameterization,
according to an axis mapping embodiment;
[0021] FIG. 5B is an illustration showing axis vector
parameterizations of the unit axes in FIG. 5A, according to an
embodiment;
[0022] FIG. 6A is an illustration showing axis vector
parameterization, according to an embodiment;
[0023] FIG. 6B is a diagram showing unit axis parameterization,
according to an embodiment;
[0024] FIG. 7 is a visualization of how axis extraction is
performed in axis mapping, according to one embodiment;
[0025] FIG. 8 shows an equation representing the negative
log-likelihood of a single observation, according to an axis
mapping embodiment;
[0026] FIG. 9 is a high-level block diagram showing major
components and functions of an MSP with axis mapping and stereonet
generation, according to one embodiment;
[0027] FIG. 10 is a diagram showing a sequence of orientations
estimated by observing rotations between sequential orientations,
directions (gravity and the Earth's magnetic field), and axes
(planar surfaces in the environment);
[0028] FIG. 11 is a block diagram showing components and functions
of a MSP with axis mapping and stereonet generation, according to
one embodiment;
[0029] FIG. 12 is an engineering drawing of a prototype MSP
according to one embodiment;
[0030] FIG. 13A is a photograph of a rock face used to evaluate the
embodiment of FIG. 12;
[0031] FIG. 13B is a stereonet corresponding to the rock face of
FIG. 13A, produced by the embodiment of FIG. 12;
[0032] FIG. 14A is a photograph of another rock face used to
evaluate the embodiment of FIG. 12; and
[0033] FIG. 14B is a stereonet corresponding to the rock face of
FIG. 14A, produced by the embodiment of FIG. 12.
DETAILED DESCRIPTION OF EMBODIMENTS
[0034] Described herein are apparatus and methods for obtaining
data corresponding to the axes of planar surfaces (i.e., the
orientation of planes) in a physical environment. The data may be
referred to as an axis map. The data may be provided as a graphical
representation, such as in a stereonet. Typically the environment
includes exposed rock. However, embodiments as described herein are
not limited thereto, and may be applied to any environment where
such data is required.
[0035] For the purpose of this disclosure, embodiments will be
described as applied to measuring the orientations of joint sets in
a rock mass. Such embodiments address weaknesses of current manual
and remote sensing approaches. Moreover, the embodiments provide
mobile measuring of joint sets to efficiently and probabilistically
provide a hands-off approach to rock mass characterization. One
embodiment considers the orientations of discontinuity planes in a
rock face as features in a map, and uses a MSP equipped with 3D
LiDAR to identify the joint sets in a rock mass.
[0036] As used herein, the term "rock mass" refers to a volume of
rock embedded in the earth.
[0037] As used herein, the term "rock face" refers to an exposed
portion of a rock mass.
[0038] As used herein, the term "axis map" refers to a
representation of the axes that define the orientations of planes
in the physical environment.
Stereonets
[0039] The orientation of a discontinuity plane is characterized by
the azimuth angle of the strike line of the plane (strike), and the
angle relative to the plane whose normal is the gravity vector
(dip), as shown in FIG. 1. Although the strike is sometimes
described by cardinal directions (e.g., N30.degree. E), this
disclosure uses the azimuth angle, which is three-digit scalar
measured clockwise from true North with the degree symbol omitted
(e.g., N30.degree. E=030). The dip is taken as the smallest angle
from the horizontal; therefore, it is always between 0.degree. and
90.degree., and is also expressed without the degree symbol. As a
result, the orientation of a discontinuity plane is fully described
by "strike/dip" (e.g., 034/77, 325/19).
[0040] One common method for visualizing strike and dip
measurements is a stereonet (i.e., a stereographic projection on
which the orientation or direction of geological features is
plotted). There are several different projections possible when
using stereonets. For example, two types of stereonets are
illustrated in FIG. 2A: a polar projection (left), and an equal
angle (Wulff) projection (right). Both projections represent strike
as the angle around the circular plot, with North (000), East
(090), South (180), and West (270). The polar projection is a graph
in polar coordinates, where the radius is the dip and the angle is
the strike; therefore, a plane is represented as a point (or pole).
A plane with orientation 030/40 is plotted as a square and a dashed
line on the polar and equal area projections, respectively.
Similarly, a plane with orientation 160/60 is plotted as a triangle
and a dash-dotted line. In the Wulff projection, the angle between
the sectors in the grid are preserved. A plane is plotted by
tracing the great circle of the dip and rotating it so that its
origin begins at the strike angle.
[0041] Discontinuity planes tend to occur in a small number of
joint sets. The correlations among the planes become evident when
plotted on a stereonet, for example, as planes belonging to the
same joint set tend to form clusters. Clustering algorithms (e.g.,
k-means, density-based spatial clustering of applications with
noise (DBSCAN)) are then used to determine the joint set membership
of individual planes. From these clusters, the mean strike and dip
angles are extracted to represent the orientation of the joint set.
This is illustrated in FIG. 2B, which shows three different joint
sets plotted on a polar stereonet prior to clustering (left) and
after clustering (right). This step may also include the rejection
of outliers (represented by stars) using either manual or
statistical methods. Planes (or axes) belonging to the same joint
set tend to appear as clusters of points in polar stereonets. From
these clusters, the mean strike and dip of each set can be
calculated (shown as a cross in each cluster). Note the uncertainty
of each plane is not usually calculated; therefore, each plane is
weighted equally in mean calculations.
[0042] Strike and dip measurements are traditionally performed
manually with a compass and an inclinometer or similar tool(s) such
as a Brunton compass. Hand measurements offer a fast, portable, and
inexpensive means of measuring strike and dip of individual planes,
but have disadvantages when a robust data set is required for
quantitative analysis, including [0043] procedural errors (e.g.,
improper use or interpretation of the tool), or sampling errors
(e.g., magnetic interference); [0044] under-sampling (i.e., not
taking enough measurements or a proper distribution of measurements
to ensure that the stereonet properly represents the rock face);
[0045] bias (e.g., choosing only planes that are easier to measure,
favouring one joint set over another); [0046] ensuring adequate
coverage of a rock face can be laborious and time consuming; [0047]
measuring inaccessible areas is difficult (e.g., the requirement of
scaffolding or rock-climbing equipment to measure tall rock faces);
[0048] safety concerns (e.g., unstable rock faces, areas where
engineering projects such as quarrying, tunnelling, or mining are
in progress). [0049] Despite these disadvantages, measuring strike
and dip by hand is widely practiced and is by far the most common
method used to produce stereonets for quantitative analysis.
[0050] Using remote sensing methods to measure the orientation of
joint sets is a relatively new and currently active field of
research. Such methods extract the discontinuity planes in a rock
face by processing 3D point clouds. The point clouds can be
obtained by photogrammetry (extracting 3D information from multiple
camera views) or by 3D LiDAR. Although photogrammetry can provide
additional information about a target (e.g., colour), 3D LiDAR
directly and usually provides a more accurate point cloud (i.e., no
additional error is introduced in combining information from
multiple sensors). In general, most approaches to date follow a
similar sequence of steps that are summarized below.
[0051] Remote sensing has a number of advantages over hand
measurements. A much larger number of planes can be measured with
much less effort, including many that may be inaccessible by hand.
Bias is reduced as the planes being measured are not manually
selected (unless, of course, this is done during plane
segmentation). As the operator does not need to interact directly
with the rock face, it is generally much safer. However, there
remains some disadvantages when using remote sensing, including:
[0052] high cost of high-resolution 3D LiDAR; [0053] the size and
weight of the sensor far exceeds that of traditional hand tools;
[0054] capturing the data required for proper joint orientation
analysis can still be laborious and time consuming due to time and
effort required for surveying and scanning; [0055] occlusions in
the data due to the orientation of planes relative to the
orientation of the sensor (in the worst case, an entire joint set
could be missed); [0056] the advantages of remotely capturing large
areas of data are restricted in closed-in areas such as underground
mines; [0057] most "off-the-shelf" software used to process the
point clouds is proprietary and expensive. [0058] In general, the
advantages of remote sensing are impeded by its high cost,
non-portability, and that it must be stationary.
Mobile Sensing Platform (MSP)
[0059] Described herein are mobile sensing platform (MSP)
embodiments for efficiently and accurately measuring the
orientation of joint sets in rock masses. The embodiments provide
the advantages of remote sensing, while overcoming many of its
disadvantages. For example, like remote sensing, MSP embodiments
measure a large number of planes without bias or physical labour.
Relative to manual and remote sensing techniques, the embodiments
provide measurements in less time and are less expensive, more
flexible to different environments, more portable, and extendable
to different platforms and sensors.
[0060] The MSP platform does not rely on any particular method of
data collection, type of sensor, or type of vehicle for mobility.
In general, an MSP has the capability to gather 3D point clouds of
a rock face, and to measure its own motion (i.e., its change in
orientation as it moves). For example, mobility of the MSP may be
achieved through a hand-held embodiment, an embodiment affixed to
or used with any type of vehicle (e.g., for one or more of
underwater, water surface, snow, land (underground and/or surface),
air, and space travel), such vehicle being operated by a human (on
board or remotely, such as a robotic vehicle or unmanned aerial
vehicle (UAV)) or operated partially or fully autonomously.
Embodiments will be described herein primarily with respect to
certain sensors; however, it will be appreciated that the invention
is not limited thereto as other types of sensors may be employed
insofar as minimum requirements for resolution and accuracy of the
point cloud are provided. For example, excellent performance is
obtained in an embodiment where a relatively inexpensive 3D LiDAR
is employed.
[0061] The most challenging aspect of measuring strike and dip
using a MSP is addressing uncertainty in sensor orientation during
observations of the rock face. In the case of a stationary sensor,
the position of the sensor is surveyed such that its orientation is
known at the time of measurement; the uncertainty in its
orientation is usually considered negligible and ignored. This is
not the case in an MSP when the sensor is constantly moving.
[0062] Although the initial orientation of an MSP might be measured
accurately, subsequent orientations of the MSP will depend on its
sensors. The sensors produce sensor signals that typically contain
"noise" which must be filtered or otherwise managed to extract
data. Additionally, a feature of the MSP is that it is not required
to be stationary during the actual creation of point clouds. To
address the problem of using potentially noisy sensor signals to
infer geometrical information about the environment (i.e., a map)
while also determining the state of the platform itself (i.e.,
localization), a batch state estimation may be used. Here, the map
is the orientation of joint sets on a targeted rock face, and the
state of the platform is its orientation. Note that because only
the orientation of the map is of interest, only the orientation of
the platform is necessary to construct the map (i.e., the position
of the platform is irrelevant). In this disclosure, measuring
strike and dip using batch state estimation will be referred to as
"axis mapping".
[0063] It is expected that MSP embodiments as described herein,
which may employ axis mapping, may be used to generate stereonets
of rock faces of at least comparable accuracy to those derived from
hand measurements and stationary remote sensing, and therefore
useful for the same types of quantitative analysis. It is noted
that a direct comparison of hand-derived stereonets and MSP
stereonets is not a measure of accuracy, as the hand-derived
stereonets are subject to the errors described above. Further,
collecting data from a rock face using a MSP is less time-consuming
and laborious than both hand measurements and stationary remote
sensing. As a result, a MSP is a viable alternative to other
methods.
[0064] It is noted that axis mapping may remain completely
independent of the MSP from which data is collected. Axis mapping
embodiments may be made generic and non-reliant on particular
sensors or vehicles, and have minimum requirements regarding the
quality of the point cloud and how motion sensing measurements
should be derived. In addition to being a convenient tool for
geological applications, axis mapping may a useful contribution to
the robotics community at least because of its approach to the
unique orientation-only batch estimation problem.
[0065] In a stationary remote sensing approach, a large
all-encompassing point cloud of a rock face is built and a plane
extraction technique is used to calculate the orientation of the
joint sets. However, that approach does not consider the special
properties of the problem being solved; specifically, the fact that
only orientations of planes are important. As a result, much of the
information in a point cloud, such as the points themselves and the
geometrical location of the extracted planes, can be discarded. The
core axis mapping algorithm is designed around this minimal
representation. The algorithm receives noisy observations of normal
vectors as input, not the point clouds themselves. Therefore, the
types of point clouds and the plane segmentation methods are kept
separate from the core algorithm. The core algorithm is agnostic to
the sensors themselves; it is only required that processed outputs
of the sensors (inputs to the algorithm) can be used to build a
graph of observations used tier batch state estimation. This
architecture allows for a unique, "orientation-only" state
estimation algorithm that deals solely with directions and
orientations and dismisses positional information. To date, no such
implementation is known to exist.
Generating the Axis Map from the Optimized State
[0066] There are two major differences between axis mapping as
described herein and conventional state estimation algorithms.
Firstly, the map in axis mapping consists of the orientations of
planes (described below), which is not a vector space. As a result,
operations on the map that are necessary when performing mapping
(e.g., perturbations, coordinate transformations, means, etc.) must
be explicitly defined to prevent violations of their topological
space. Next, the physical environment being observed has multiple
instances of the same feature in the map. All discontinuity planes
in a rock face with (nearly) the same orientation are part of the
same joint set. That is, there is no distinction between observing
two different discontinuity planes if they belong to the same joint
set. The joint set itself is the feature in the map, not the
individual planes. This is a fundamental difference between axis
mapping and conventional state estimation algorithms, as it affects
how the problem must be formulated. This difference is illustrated
in FIG. 3, which shows that in landmark-based mapping (top), each
landmark is unique; there is a one-to-one mapping between map
entries and landmarks in the environment. In axis mapping (bottom),
map entries exist in multiple locations in the environment. Also,
due to the natural variations of rock faces, the orientation of
planes belonging to the same joint set vary. That is, the lines
marked by .sup..fwdarw.n.sub.1 in this 2D illustration belong to
the same joint set but are not oriented identically. Additionally,
there are natural variations in the orientation of individual
discontinuity planes in a joint set. Therefore, the "true"
orientation of a joint set is a distribution, which must be
considered when attempting to associate a newly observed
discontinuity plane with a joint set.
The Axis Mapping State
[0067] The axis mapping state consists of orientations and axes.
Many different parameterizations of rotations exist; however, it is
well known that all minimal parameterizations (i.e., the number of
parameters is equal to the number of degrees of freedom) have at
least one singularity. The set of all axes form the unit sphere
S.sup.2. An axis is the unordered pair of directions diametrically
opposed the unit sphere, or equivalently, a single point on the
unit hemisphere. Like rotations, minimal parameterizations of axes
have at least one singularity.
[0068] Axis mapping parameterizes rotations as both unit
quaternions (global parameterization) and rotation vectors (local,
vector-like parameterization). FIG. 4 is an illustration of a
rotation vector .theta.. Geometrically, rotation vector space is a
ball of radius .pi.. The length of the rotation vector represents
the angle of rotation .theta., and its direction corresponds to the
axis of rotation a. The projection of the rotation vector to the
surface of the ball is shown to help visualize the space as a solid
ball. The rotation vector .theta.=[.theta..sub.1 .theta..sub.2
.theta..sub.3].sup.T is parameterized by its three scalar
components in this space. The rotation vector is "pseudo vector
space" that is required to perform state estimation.
[0069] Axes are parameterized as both unit axes (global
parameterization) and axis vectors (local, vector-like
parameterization). According to one embodiment, global
parameterization (FIG. 5A) is used to represent axes that are free
of singularities and is defined for all axes. When axes are
compared and subtracted from each other, this is done using unit
axes and the difference is converted into an axis vector (see FIG.
5B). Axis vector parameterization according to another embodiment
is shown in FIG. 6A, and FIG. 6B shows the unit axis
parameterization. The projection of the unit axis onto the plane of
the hemisphere is the vector part .kappa., and its component along
the axis of the hemisphere (3) is the scalar part .lamda.. The
angle .PHI. between the axis of the hemisphere and the unit axis,
and the normalized vector part r, form the axis-angle
parameterization of an axis, and their product .PHI.:=.PHI.r form
the axis vector parameterization. The identity unit axis o is the
unit axis along the axis of the hemisphere.
[0070] Unit quaternions and unit axes are global parameterizations
of their respective spaces because they vary continuously for
continuous changes in the states they represent. Rotation vectors
and axis vectors are local parameterizations because they only vary
continuously for continuous local changes from a reference state.
Put differently, given a reference rotation or axis, not all
rotations and axes relative to the reference are well-defined by
local parameterizations due to singularities. Axis mapping
alternates between these two parameterizations: the state is
represented by a global parameterization, while the state
estimation algorithm calculates local perturbations to the state
with the local parameterization. Because state perturbations and
observation errors tend to be local, the issues associated with the
local parameterization are avoided.
[0071] FIG. 6A is an illustration of the axis vector
parameterizations. Axis vectors are one of the two
parameterizations of axes used in axis mapping (the other being
unit axes (FIG. 6B)). The axis vector is a "pseudo vector space"
that is required to perform state estimation. Geometrically, axis
vector space is a flattening of the unit hemisphere to a disc of
radius .pi./2. The axis vector .PHI. has length .PHI. in the
direction r. It is parameterized by its two scalar components
.PHI.=[.PHI..sub.1 .PHI..sub.2].sup.T in this space.
[0072] FIG. 7 is a visualization of how axis extraction is
performed in axis mapping. This describes how a point cloud is
transformed into a list of axis observations. First, a voxel filter
reduces the number of points in the point clouds. Next, outliers
are removed based on the mean distance to their neighbouring
points. Next, a robust variant of principal component analysis
(PCA) is used to estimate the normal vector to surface being
measured. Finally, the curvature of the surface being measured is
estimated, and points with larger curvatures are discarded.
Data Collection and Observations
[0073] The MSP is equipped with sensors that sense/measure
distance, gravity, the direction of the Earth's magnetic field, and
angular velocity. For example, the sensors may comprise a 3D range
sensor (e.g., a LiDAR), a three-axis accelerometer, three-axis
gyroscope, and three-axis magnetometer. Data is collected by moving
the MSP through a trajectory in the test environment. The
trajectory is selected to ensure that most or all of the flat
surfaces of interest are scanned by the range sensor. The
orientation of the MSP is estimated at discrete moments of the
trajectory. At each orientation, the sensor suite on the MSP
observes the direction of gravity (using the accelerometers), the
direction of the Earth's magnetic field (using the magnetometers),
and/or the axes of flat surfaces in the environment (using the
range sensor). Additionally, the rotation of the MSP between
sequential orientations is also observed (using the
gyroscopes).
[0074] Each type of observation is predicted based on the current
estimate of the orientation of the MSP and an observation model.
These predictions are compared against the actual sensor
observations and the difference between them is the error of the
observation. Axis mapping determines the optimal sequence of
orientations of the MSP that minimizes these errors.
Associating Axes Observed at Different Orientations
[0075] The axes extracted from measurements by the 3D range sensor
are all expressed in the coordinate frame of the sensor. To
associate observations from different observations, the axes are
first transformed to a common shared frame. Using the initial
estimate of the sequence of orientations of the MSP, all the axis
observations are transformed to the global coordinate frame. At
this point, similar observations are clustered together and marked
as observations of the same planar surface in the environment.
Optimizing the Axis Mapping State
[0076] The negative log-likelihood of an observation is its squared
error (with respect to its prediction) proportional to the inverse
of its covariance matrix (i.e., its uncertainty). The goal of axis
mapping is to determine the optimal estimate of the state that
minimizes the negative log-likelihood of all observations
simultaneously. The sum of all the negative log-likelihoods is
calculated using a cost function. The state is optimized by
iteratively solving for the optimal perturbation of the state
estimate that minimizes the linearized cost function. See, for
example, FIG. 8. It is necessary to linearize the cost function
because the observation models are all nonlinear. Also, because the
observations and the state are not part of a vector-space (e.g.,
rotations and axes cannot be treated as vectors), the optimal
perturbation is applied by first converting it to its global
parameterization. Additionally, linearizing the cost function must
also consider the spaces in which the observations reside. The
actual calculation of the optimal perturbation is determined using
a nonlinear least-squares algorithm.
[0077] For example, FIG. 8 shows an equation representing the
negative log-likelihood of a single observation. The optimization
function minimizes the sum of the negative log-likelihood of all
the observations simultaneously. That is, the result of the
equation is calculated for every observation (i.e., every
measurement of the direction of gravity, the earth's magnetic
field, rotations between orientations, and axes extracted from
point clouds), and the results are summed to get the total cost of
all the observation errors. An optimization algorithm then
determines the best way to change (i.e., perturb) the state (i.e.,
the estimated sequence of orientations) such that the total cost is
as small as possible.
Generating the Axis Map from the Optimized State
[0078] The optimized state contains the best estimate of the
orientation of the MSP at a sequence of steps along its trajectory.
At each of these orientations, a number of axes were extracted from
a measurement of the 3D range sensor. Using the orientation from
which the measurement was made, each axis is rotated into the
global coordinate frame. This rotation is performed using the
quaternion rotation operator, which performs a rigid transformation
of the axis. The resulting axis map can be visualized as a
stereonet if required by converting each axis to a strike and dip
parameterization.
Media
[0079] Embodiments may comprise programmed media for use with a
computer, the programmed media comprising a computer program stored
on non-transitory storage media compatible with the computer, the
computer program containing instructions to direct the computer to
perform one or more of: receive at least one sensor signal from at
least one sensor associated with a MSP; process the one or more
sensor signals and generate observations of axes in the environment
for a sequence of time steps; estimate orientation of the MSP for
each time of the sequence of time steps, identify observed axes at
each orientation, and associate similar axes; link the
orientations, the axes in the environment, and the directions of
gravity and the Earth's magnetic field, such that each observation
is predicted based on the estimates of the orientations, and
optimize an estimate of the orientations; and output an axis map
from the optimized orientation estimates.
[0080] In one embodiment the programmed media directs the computer
to receive sensor signals from sensors comprising a range sensor, a
three-axis accelerometer, a three-axis gyroscope, and a three-axis
magnetometer.
[0081] In another embodiment the programmed media directs the
computer to receive data corresponding to observations of axes in
the environment for a sequence of time steps and estimates of
orientation of the MSP for each time of the sequence of time steps;
identify observed axes at each orientation, and associate similar
axes; link the orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field, such that
each observation is predicted based on the estimates of the
orientations, and optimize an estimate of the orientations; and
output a stereonet from the optimized orientation estimates.
[0082] Embodiments are further described by way of the following
non-limiting Examples.
EXAMPLE 1
[0083] This example describes a generalized MSP including an
algorithm that may be used to obtain an axis map (i.e., a list of
dominant planar axes) in an environment, and generate a
representative output, such as an axis map (e.g., a stereonet).
Typically the environment is a rock face, although the embodiment
may be applied to other environments. As noted above, the MSP may
be a handheld wand/device, a mobile robot, a UAV, or other robotic
or non-robotic platform.
[0084] Referring to FIG. 9, the MSP is equipped with sensors 20
that sense/measure distance, gravity, the direction of the Earth's
magnetic field, and angular velocity. For example, the sensors may
include a range sensor, a three-axis accelerometer, a three-axis
gyroscope, and a three-axis magnetometer. The MSP is moved through
the environment in such a way that all planes to be mapped are
captured by the field of view of the range sensor. The data from
all the sensors is then processed 22 to produce a time sequence of
observations. An initial estimate of the orientation of the MSP is
calculated 24 for the sequence of time steps and the observed axes
at each orientation are associated with each other. For example, a
most likely sequence of orientations, e.g., depicted as the
coordinate frames in FIG. 10, may be estimated by observing
rotations between sequential orientations, directions (gravity and
the Earth's magnetic field), and axes (planar surfaces in the
environment). Linking nodes (e.g., a graph) is built 26 linking the
estimated orientations, the axes in the environment, and the
directions of gravity and the Earth's magnetic field. Each
observation (an edge in the graph) is predicted based on the
initial estimates of the orientations, and errors between the
predictions and the observations are minimized 28, producing an
optimal estimate of the orientations. An output, such as a
stereonet, is generated 30 by transforming the observed axes to the
global coordinate frame using the optimized orientation
estimates.
EXAMPLE 2
[0085] This example describes a more detailed embodiment based on
the generalized embodiment of Example 1. The features described
herein, with reference to FIG. 11, may be included in a MSP and may
be used to obtain an axis map in an environment such as a rock
face, and generate an output such as a stereonet. [0086] (i) The
MSP is equipped with sensors including a range sensor 30, a
three-axis accelerometer 32, a three-axis gyroscope 34, and a
three-axis magnetometer 36. The MSP is moved through the
environment in such a way that all planes to be mapped are captured
by the field of view of the range sensor.
[0087] Each sensor has minimal requirements that must be met to be
used for axis mapping, which are described below. The data output
from certain sensors is processed before being used for axis
mapping. The range sensor 30 is used to produce point clouds (i.e.,
an array of points in 3D space). The point clouds are generated at
a high enough rate relative to the motion of the MSP in order to
consider all points in a single point cloud to have been measured
from a single orientation of the MP. The three-axis accelerometer
32 measures the acceleration of the MSP in three perpendicular
axes. It may comprise three accelerometers (one per axis). The
three-axis gyroscope 34 measures the angular velocity of the MSP in
three perpendicular axes. It may comprise three gyroscopes (one per
axis). The frequency of the sensor is high enough such that that
the angular velocity of the MSP may be assumed to be constant
between measurements. The three-axis magnetometer 36 measures the
local magnetic field in the proximity of the sensor in three
perpendicular axes. It may comprise three magnetometers (one per
axis). The accelerometer, gyroscope, and magnetometer may be
contained in a single sensor (e.g., an inertial measurement unit
(IMU)). If the coordinate frames of the accelerometer, gyroscope,
and magnetometer are not aligned, the rotation between their
respective coordinate frames must be known.
[0088] Axes of planar surfaces are extracted 40 from the point
cloud measured by the range sensor. This involves first removing
outliers in the point cloud, estimating the axis at each point in
the point cloud, and then removing points whose axes are determined
not to be part of a planar surface. Similar axes are then clustered
together 54 using, e.g., the DBSCAN algorithm (M. Ester, et al., "A
density-based algorithm for discovering clusters in large spatial
databases with noise," in Proceedings of the 2nd International
Conference on Knowledge Discovery and Data Mining. AAAI Press,
1996, pp. 226-231) to generate a small number of axes representing
all the planar surfaces measured by the sensor.
[0089] The output of the accelerometer is normalized 42 to
determine the direction of the external accelerations acting on the
MSP. This direction is assumed to be the direction of gravity, with
extra uncertainty in the observation being included if additional
external forces acting on the MSP are detected. The output of the
gyroscope is integrated 44 to estimate changes in orientation of
the MSP. The uncertainty of this observation is proportional to the
length of time between measurements made by the range sensor. The
output of the magnetometer is normalized to determine the direction
of the Earth's magnetic field. The magnetometer is calibrated
beforehand to compensate for soft and hard iron distortions. [0090]
(ii) An initial estimate of the 3D orientation of the MSP in the
global coordinate frame (North, East, down) is calculated 50, 52
from the observed directions of gravity and the Earth's magnetic
field using, e.g., the factored quaternion algorithm (FQA) (X. Yun,
et al. "A simplified quaternion-based algorithm for orientation
estimation from earth gravity and magnetic field measurements",
IEEE Transactions on Instrumentation and Measurement, 2008, vol.
57, pp. 638-650). An orientation is estimated at the time of each
measurement by the range sensor. [0091] (iii) After an initial
estimate of the orientation of the MSP is available at each range
sensor measurement, all axes extracted from the point clouds are
transformed to the global reference frame. At this point, similar
axes are clustered together 54 (i.e., they are associated) to form
a small number of distinct axis observations. The axes observed at
each orientation are marked with which axis they are observing.
[0092] (iv) A graph is generated 56 that links nodes (orientations
of the MP, planar axes in the environment, and the constant
directions of gravity and the Earth's magnetic field in the global
coordinate frame) with edges (one edge per observation). There are
four types of observations: (a) rotations between consecutive
orientations (from integrating the gyroscopes), (b) planar axes in
the environment (from processing the point clouds generated by the
range sensor), (c) the direction of gravity at each orientation
(from normalizing the accelerometers), and (d) the direction of the
Earth's magnetic field at each orientation (from normalizing the
magnetometers; 58. Each observation is now associated with an
orientation in the graph. [0093] (iv) A prediction of each
observation is generated 60 from the initial guess of the
orientations. For example, a prediction of the integrated gyroscope
observation of the rotation between sequential orientations is the
rotational difference between the initial guesses of those
orientations. The difference between observations and their
predictions is the error of the observation 62. The goal of error
minimization 64 is to determine the orientations that result in the
minimum squared error of all the observations simultaneously. As an
example, the Levenberg-Marquardt algorithm (W. H. Press, et al.,
Numerical Recipes: The Art of Scientific Computing, 3rd ed.,
Cambridge University Press, 2007) may be used for this purpose. The
result is an optimized estimate 66 of the sequence of orientations
undergone by the MP during data collection. [0094] (v) Given the
optimized estimate of the sequence of orientations resulting from
error minimization, an axis map in the global frame is generated
68. A small number of axes were observed at each orientation (i.e.,
the axes resulting from axis extraction, as described in (i). The
axes are rotated to the global coordinate frame using the optimized
orientations. In other words, now that the orientation of the MSP
is known at the time of each range sensor measurement, the
measurements themselves can be expressed in the global coordinate
frame. A stereonet is simply one parameterization these
measurements. The axes are converted to points and plotted on a
stereonet 70 via a change of variables.
EXAMPLE 3
[0095] A prototype MSP was constructed using substantially off the
shelf parts, as shown in the engineering drawing of FIG. 12. Main
components are listed in Table 1 (item numbers as in FIG. 12). The
MSP was interfaced with an Apple iPad tablet computer.
TABLE-US-00001 TABLE 1 Parts list for MSP prototype PARTS LIST ITEM
QTY PART NUMBER 1 1 Aluminum tube 2 1 KinectOne 3 2 Handle 4 1
3DM-GX3-25-IMU 5 2 ipad_mount 6 1 iPAD 4 8 1 hinge_block 9 1
kinect_leg 10 1 bottom_leg 12 2 ipadleg 13 9 0.25-28screw0.5 in 14
10 0.25-28screw1 in
[0096] Two rock faces (FIGS. 13A and 14A) near Kingston, Ontario,
Canada were scanned with the MSP. A field notebook and compass are
included in the photograph of FIG. 13A for scale. The stereonets of
FIGS. 13B and 14B, respectively, were produced as outputs.
[0097] All cited publications are incorporated herein by reference
in their entirety.
EQUIVALENTS
[0098] While the invention has been described with respect to
illustrative embodiments thereof, it will be understood that
various changes may be made to the embodiments without departing
from the scope of the invention. Accordingly, the described
embodiments are to be considered merely exemplary and the invention
is not to be limited thereby.
* * * * *